Impact compression of alkali metals: Computer-aided simulation

This article describes a method for calculation of the potential of the embedded atom model (EAM), suitable for calculation of the properties of alkali metals in highly compressed states. For the first time, sequential consideration of the thermal energy and thermal pressure of collective electrons has been introduced into the EAM flowchart. The parameters of the EAM potential have been calculated, which make it possible to obtain good agreement in terms of pressure and energy for five alkali metals under impact compression. The properties of the molecular dynamic models of alkali metals at 300 and 0 K are compared with the data of static compression. The agreement between them is sufficient up to pressures of 15–20 GPa, and at higher compression rates divergences become significant. A lack of experimental data makes it impossible to understand whether the reason for these divergences is incomplete adequacy of the EAM potential or systematic errors contained in the experimental data in the range of high pressures. The proposed potentials make it possible to calculate the thermodynamic, structural, and diffusion properties of alkali metals in highly compressed states at temperatures up to 20000–30000 K.     

Computer simulation of aluminum in the high-pressure range

A technique is developed for constructing crystalline aluminum models with the potential of the embedded atom model (EAM) obtained earlier in [1] and corrected for describing strongly compressed states. This technique was applied for aluminum in the range of high pressures created by strong shock waves. Using the method of molecular dynamics (MD) and EAM potential, it is possible to achieve good agreement with experiment as far as the structure, density, and energy of the metal along the shock adiabat up to a pressure of ∼260 GPa and temperature of ∼11500 K are concerned. Several models have been constructed in the high-pressure range at absolute zero temperature, and the adequacy of the Grüneisen model has been evaluated. Models for liquid aluminum have been constructed at temperatures up to 800 K, and the parameters of the critical point (∼7050 K, density of 0.675 ± 0.034 g/cm³, pressure of 0.325 ± 0.02 GPa, Z = pV/RT = 0.22 ± 0.03) have been determined.     

Application of the embedded-atom method to liquid copper

A procedure for calculating the embedded-atom method (EAM) potential with the use of diffraction data for the metal near its melting point has been applied to copper at temperatures from 1423 to 7400 K. In optimizing the parameters of the EAM potential, we used the pair correlation functions of copper at 1423 and 1873 K, the thermodynamic properties of liquid copper under ordinary conditions, and flash heating and shock compression results. Molecular dynamics simulation with the EAM potential adequately represents the thermodynamic properties and structural characteristics of liquid copper up to 1873 K. The simulated 1423-K bulk modulus is close to the experimentally determined one. At low pressures, the self-diffusion coefficient rises as a power law function of temperature with an exponent close to 2.10. The simulated melting point of copper, 1384 ± 3 K, is close to the actual one. Simulations were performed at temperatures of up to 7400 K and densities a factor of 1.6 higher than the normal one. The melting point was evaluated at pressures of up to 50 GPa. The EAM potential obtained is suitable for the liquid phase but fails to accurately describe properties of crystalline copper.     

Computer simulation of liquid zinc

An embedded atom model potential for zinc has been developed, which makes it possible to calculate liquid zinc properties both under normal pressure and in strongly compressed states using the molecular dynamics method. In order to calculate the potential, the data on density, energy, and compressibility of liquid zinc and the data on shock compression of zinc were used. Pair contribution to the potential and the embedding potential are represented by analytical functions. Liquid zinc properties are calculated at temperatures up to 1500 K. The values of energy, bulk compression modulus, and self-diffusion coefficient, as well as pair correlation functions at T < 1000 K, agree well with the experiment. The electron contribution to the thermal capacity at those temperatures is not high. Zinc models are constructed for densities up to 15.86 g/cm³ and pressures up to 773 GPa. Zinc models melt in the case of shock compression at compression rates of V/V ₀ < 0.7 and temperatures above 1900 K. A significant contribution of electron excitation energy to the zinc energy is observed at temperatures above 20000 K. The estimated average surplus thermal capacity of electrons at 30000–50000 K is ∼12 J/mole K. Discrepancies between the molecular dynamic calculation and the Gruneisen model at low temperatures are relatively low; however, they rise as temperature increases. A series of zinc nanocluster models with magic sizes of 55 and 147 atoms is constructed. The clusters have an amorphous structure with slightly lower energy than that of icosahedral or cuboctahedral configuration, after cooling from 600 to 10 K. The surface energy of zinc at T = 0 calculated based on the dependence of energy of clusters on size is 1.3 J/m².     

Application of the embedded atom model to liquid metals: Liquid sodium

The procedure for the calculation of the embedded atom model (EAM) potential for liquid metal, which involves the use of diffraction data on the structure of material in the vicinity of the melting point, is applied to sodium. In fitting the parameters of EAM potential, use is made of the data on the structure of sodium at 378, 473, and 723 K, as well as on the thermodynamic properties of sodium at pressures up to 96 GPa. The use of the method of molecular dynamics (MD) and of the EAM potential produces good agreement with experiment as regards the structure, density, and potential energy of liquid metal along the p ? 0 isobar at temperatures up to 2300 K, as well as along the shock adiabat up to pressures of ～100 GPa and temperature of ～30 000 K. The melting temperature of bcc model of sodium with EAM potential is equal to 358 ± 1 K and close to real. The predicted value of bulk modulus at 378 K is close to the actual value. The self-diffusion coefficients under isobaric heating increase with temperature by the power law with exponent of 1.6546. The values of pressure, energy, heat capacity, and the temperature coefficient of pressure are calculated in a wide range of densities. The compression to 45–50% of normal volume causes a variation of the structure of liquid; this results in the emergence of atoms with a small radius of the first coordination sphere (～2.1 Å) and low coordination number, which form connected groups (clusters). Their concentration increases with decreasing volume and increasing temperature. The pre-peak of pair correlation functions, the height of which increases with heating, corresponds to these atoms. In the region of variation of the structure, the pressure decrease under isochoric heating follows the pattern of water anomaly.     

Electron contribution to energy of alkali metals in the scheme of an embedded atom model

The behavior of the energy of molecular dynamics models of alkali metals constructed using the embedded atom potential at high temperatures is discussed. Pair potentials and embedding potentials for lithium, sodium, potassium, rubidium, and cesium are presented as uniform analytical expressions. If the parameters of the potential of the embedded atom model (EAM) are selected based on the known dependence of the density of liquid metal on temperature, then, as temperature approaches the critical one, the actual energy increases faster than the energy of the models in all cases. The thermal contribution of electron gas to the energy of metal is considered as the cause of the discrepancy. It is shown that it is possible to eliminate the discrepancy between energies of models and the actual metal at high temperatures, if the energy of thermal excitation of electrons is taken into consideration. The difference between the actual energy of metal and the energies of EAM for liquid Li, K, and Cs is almost equal to the contribution of the thermal energy of electrons. The thermal energy of electrons is taken into account in analysis of data obtained using shock compression.     

Molecular-dynamic simulation of the thermophysical properties of liquid uranium

The procedure for the calculation of the embedded atom model (EAM) potential, which involves the use of data on the structure of liquid metal in the vicinity of the melting temperature and of the results of impact tests, is applied to uranium. The use of the method of molecular dynamics and of the EAM potential produces good agreement with experiment as regards the structure, density, and potential energy of liquid metal at temperatures up to 5000 K, as well as along the shock adiabat up to pressures of ≈360 GPa. The thermodynamic properties of solid (bcc) and liquid uranium are determined at pressures up to 470 GPa and temperatures up to 12 000 K. The predicted value of bulk modulus of liquid at 1406 K is close to the actual value. The self-diffusion coefficient under isobaric heating increases with temperature by the power law with exponent of ≈2.103. The Stokes—Einstein relation is used to determine the dynamic viscosity at temperatures up to 6000 K. The obtained potential is not quite adequate for describing crystalline uranium under normal conditions. The melting temperature of uranium with EAM potential is equal to 1455 ± 2 K and somewhat higher than real. The melting temperature monotonically increases with pressure and reaches the value of 7342 K at 444 GPa. For obtaining agreement with experimental data for energy of uranium along the p = 0 isobar, it is assumed that an additional contribution to energy emerges at elevated temperatures, which is due to excitation of atomic electrons and leads to a high heat capacity: it may be as high as almost 100 kJ/mol at 5000 K. This contribution further causes a high heat capacity of highly compressed states of uranium.     

Molecular-dynamics simulation of the high-pressure properties of rubidium

An embedded-atom potential for rubidium has been calculated with the parameters chosen with the use of the results of the static tests at a temperature of 300 K and pressures up to 45 GPa, as well as the results of the shock tests at pressures up to 39 GPa. The molecular-dynamics simulation has been performed for temperatures of 300–10 000 K and pressures up to ∼94 GPa. The potential determined from the shock-test data does not provide complete agreement with the static data for 300 K. The pressure, energy, and specific heats C _V and C _p have been calculated for the compression up to 20% of the normal pressure and for temperatures up to 10 000 K. The derivative (∂p/∂T) _V is positive for all of the molar-volume and temperature values except for a compression ratio of 30%. Compression up to a factor of 2.5 or more is accompanied by the partial amorphization of the models, which is enhanced with heating. The calculations of the temperature along the Hugoniot curve under the assumption that the Grüneisen parameter and adiabatic compression modulus are independent of the temperature provide an incorrect molar-volume dependence of the pressure at 0 K.     

Application of the embedded atom model to liquid metals: Liquid lithium

The procedure for the calculation of the embedded atom model (EAM) potential for liquid metal, which involves the use of diffraction data on the structure of material in the vicinity of the melting point, is applied to lithium. In fitting the parameters of EAM potential, use is made of data on the structure of lithium at 463, 523, and 868 K, as well as on the thermodynamic properties of lithium at temperatures up to 3400 K. The use of the method of molecular dynamics (MD) and of the EAM potential enables one to obtain good agreement with experiment as regards the structure, density, and potential energy of liquid metal at temperatures up to 3000 K, as well as along the shock adiabat up to pressures of ～260 GPa. The predicted value of bulk modulus at 463 K is close to the actual value. The self-diffusion coefficients under isobaric heating increase with temperature by the power law with exponent of 1.7182. The obtained potential is inadequate for describing crystalline lithium. The predicted melting temperature of lithium with EAM potential is 428 ± 2 K and is close to real temperature.     

Application of the embedded-atom method to liquid Fe-S solutions

A procedure (proposed earlier to describe liquid Fe) for calculating the embedded-atom method (EAM) potential with the use of structural and thermodynamic data for the metal near its melting point has been applied to liquid Fe-S solutions at temperatures of up to 5000 K and pressures of up to 360 GPa. Molecular dynamics simulations have been carried out for solutions with 0–18 at % S with the EAM potential at temperatures from 1820 to 5000 K and densities from 10.69 to 12.28 g/cm³. We have calculated the thermodynamic, structural, and diffusion properties and estimated the viscosity of noncrystalline phases. At a pressure near 360 GPa and a temperature of 5000 K, pure iron crystallizes spontaneously, while the solutions of sulfur in iron behave as high-viscosity liquids or amorphous phases with a self-diffusion coefficient on the order of 10^?7 cm²/s and a viscosity of up to tens of Pa s. As the sulfur content increases from 0 to 6.2 at %, the viscosity first decreases and then rises. During long-term relaxation, the model of an Fe-S solution may turn into a crystalline-like state. The origin of marked discrepancies between ab initio and EAM simulation results is discussed.     

Computer simulation of copper and silver under shock compression conditions

A correction to the embedded atom method potentials for copper and silver is proposed which ensures good agreement between molecular dynamics simulation results and experimental data on the thermodynamic properties of Cu and Ag under shock compression conditions (at pressures of up to 1473 GPa in the case of copper and up to 478 GPa in the case of silver). The potentials are represented in analytical form. The calculations take into account the contributions of the valence electrons to the energy and pressure of the metals. This reduces the simulated temperature on the Hugoniot adiabat (by 30% in the case of copper and by a factor of 1.5–2 in the case of silver) relative to estimates in the Grüneisen model.     

Shock-wave synthesis of diamond nanofibers and their structure

Diamond nanofibers produced by high-temperature shock compression of graphite nanofibers in the presence of KCl at pressures of 25–35 GPa and temperatures of 3000–3500 K have been considered. The synthesized fibers have been shown to consist of randomly oriented nanograins of diamond with the amorphous phase impurity, whose content decreases as the impact compression pressure increases.     

Solidification of the melts of metals and liquids in shock waves and quasi-isentropic and isentropic compression

Interest in the study of solidification under shock, quasi-isentropic, and isentropic compressions from the initial liquid state of matter has recently been rekindled. Rapid solidification and crystallization are associated with overcooling under dynamic compressions in the region of rather high pressures. Experimental investigations of solidification due to single and multiple shocks and isentropic compressions were conducted on melts of bismuth and tin; at melting temperatures or higher; and on water, carbon tetrachloride, benzene, and other substances under normal conditions. On the basis of the experimental data on viscosity under the shock compression of water and mercury, the possibility of their crystallization beyond the shockwave front was confirmed.     

On the shock compression of polycrystalline metals

At the present time, materials are being considered for use in increasingly extreme environments; extreme in terms of both the magnitude of the imposed pressures and stresses they encounter and the speed of the loading applied. Recent advances in understanding the continuum behaviour of condensed matter have been made using novel loading and ultrafast diagnostics. This insight has indicated that in the condensed phase, the response is driven by the defect population existing within the microstructure which drives plastic flow in compression as well as damage evolution and failure processes. This article discusses shock compression results, focusing upon research conducted on cubic-structured metals but also giving an overview of results on hexagonal-close-packed (HCP) metals and alloys. In the past, shock physics has treated materials as homogeneous continua and has represented the compressive behaviour of solids using an adaptation of solid mechanics. It is clear that the next generation of constitutive models must treat physical mechanisms operating at the micro- and mesoscale to adequately describe metals for applications under extreme environments. Derivation of such models requires idealized modes of loading which limits the range of hydrostatic or impact driven experimental techniques available to four principle groups. These are laser-induced plasma loading, Z pinch devices, compressed gas and powder-driven launchers and energetic drives and diamond anvil cells (DACs). Whilst each technique or device discussed brings unique advantages and core competencies, it will be shown that launchers are most capable of covering the spectrum of important and relevant mechanisms since only they can simultaneously access the material microstructural ‘bulk’ dimensions and timescales that control behaviour observed at the continuum. Shock experiments on a selection of metals whose response is regarded as typical are reviewed in this article, and sensors and techniques are described that allow the interpretation of the compression that results from idealized step loading on a target. Real-time imaging or X-ray techniques cannot at present access bulk states at the correct microstructural resolution, over a macroscopic volume or at rates that would reveal mechanisms occurring. It is controlled recovery experiments that provide the link between the microstructure and the continuum state that facilitates understanding of the effect of mesoscale properties upon state variables. Five metals are tracked through various shock-loading techniques which show the following characteristic deformation features; a low Peierls stress and easy slip allow FCC materials to develop dislocation cells and work-harden during the shock process, whereas the higher resistance to dislocation motion in BCC-structured materials and the lower symmetry in HCP metals slows the development of the microstructure and favours deformation twinning as an additional deformation mechanism to accommodate shock compression. Thus not only energy thresholds, but also operating kinetics, must be understood to classify the response of metals and alloys to extreme loading environments. Typical engineering materials possess a baseline microstructure but also a population of defects within their volumes. It is the understanding of these statistical physical relationships and their effects upon deformation mechanisms and defect storage processes that will drive the development of materials for use under extreme conditions in the future.     

Thermophysical properties ofm-cresol as a function of temperture (303 to 503 K) and pressure (0.1 to 400 MPa)

Measured and derived thermophysical properties ofm-cresol are reported for pressures up to 400 MPa at temperatures from 303 to 503 K. Isobaric thermal expansivities were measured by pressure-scanning calorimetry from 303 to 503 K and 0.1 to 400 MPa. The specific volume at 353 K was determined by pycnometry at atmospheric pressure and calculated from isothermal compressibilities measured as a funtion of pressure up to 400 MPa. Specific volumes at other temperatures and pressures are calculated from isothermal compressibilities measured as a function of pressure up to 400 MPa. Specific volumes, isothermal compressibilities, thermal coefficients of pressure, and isobaric and isochoric heat capacities at pressures up to 400 MPa are derived at several temperatures. The effects of pressure on the isobaric heat capacities ofm-cresol,n-hexane, and water are compared. The effects of self-association ofm-cresol are apparent in both the thermal expansivity and the heat capacity data.     

Thermal conductivity and heat capacity of solid nabr under pressure

Using the transient hot-wire method, measurements were made for solid NaBr of both the thermal conductivity and the heat capacity per unit volume. The measurements were performed in the temperature range 100 to 400 K and at pressures up to 2 GPa. An adiabatic compression technique allowed the determination of the thermal expansivity as a function of pressure at room temperature. The heat capacity did not vary with pressure. Analysis of the thermal conductivity data showed that it can be described adequately by the Leibfried-Schlömann formula. For temperatures up to 400 K only acoustic modes needed to be taken into account. A small contribution of optic modes to the heat transport might be apparent at the highest temperatures.     

Study of the Effects of Temperature and Pressure on the Thermodynamic and Acoustic Properties of 2-Methyl-1-butanol at Temperatures from 293K to 318K and Pressures up to 100MPa

The speeds of sound in 2-methyl-1-butanol were measured at temperatures from 293K to 318K and pressures up to 101MPa. The densities were measured in the same temperature range under atmospheric pressure. The isobaric specific heat capacities were measured at atmospheric pressure and temperatures from 284K to 355K. The densities, isobaric heat capacities, isobaric thermal expansions, isentropic compressibilities, isothermal compressibilities, and internal pressures as functions of temperature and pressure were calculated using the experimental speeds of sound under elevated pressures together with the densities and heat capacities at atmospheric pressure. The effects of temperature and pressure on the isobaric thermal expansion and internal pressure of 2-methyl-1-butanol are discussed and compared with those of pentan-1-ol, 2-methyl-2-butanol, and pentan-3-ol.